Photon upconversion is a photophysical process in which two lowenergy photons are converted into one high-energy photon. Photon upconversion has broad appeal for a range of applications from biomedical imaging and targeted drug release to solar energy harvesting. Current upconversion nanosystems, including lanthanide-doped nanocrystals and triplet−triplet annihilation molecules, have achieved upconversion quantum yields on the order of 10−30%. However, the performance of these materials is hampered by inherently narrow absorption cross sections and fixed energy levels originating in atomic, ionic, or molecular states. Semiconductors, on the other hand, have inherently wide absorption cross sections. Moreover, recent advances enable the synthesis of colloidal semiconductor nanoparticles with complex heterostructures that can control band alignments and tune optical properties. We synthesize and characterize a three-component heterostructure that successfully upconverts photons under continuous-wave illumination and solarrelevant photon fluxes. The heterostructure is composed of two cadmium selenide quantum dots (QDs), an absorber and emitter, spatially separated by a cadmium sulfide nanorod (NR). We demonstrate that the principles of semiconductor heterostructure engineering can be applied to engineer improved upconversion efficiency. We first eliminate electron trap states near the surface of the absorbing QD and then tailor the band gap of the NR such that charge carriers are funneled to the emitting QD. When combined, these two changes result in a 100-fold improvement in photon upconversion performance.

A new mathematical representation for nonlinear viscoelasticity is presented based on application of the Volterra series expansion to the general nonlinear relationship between shear stress and shear strain history. This theoretical and experimental framework, which we call Medium Amplitude Parallel Superposition (MAPS) Rheology, reveals a new material property, the third order complex modulus, which describes completely the weakly nonlinear response of a viscoelastic material in an arbitrary shear flow. In this first part, we discuss several theoretical aspects of this mathematical formulation and new material property. For example, we show how MAPS measurements can be performed in strain or stress controlled contexts and provide relationships between the weakly nonlinear response functions measured in each case. We show that the MAPS response function is a super-set of the response functions that have been previously reported in medium amplitude oscillatory shear and parallel superposition rheology experiments. We also show how to exploit inherent symmetries of the MAPS response function to reduce it to a minimal domain for straightforward measurement and visualization. We compute this material property for a few constitutive models to illustrate the potential richness of the data sets generated by MAPS experiments. Finally, we discuss the MAPS framework in the context of some other nonlinear, time-dependent rheological probes and explain how the MAPS methodology has a distinct advantage over these others because it generates data embedded in a very high dimensional space without driving fluid mechanical instabilities, and is agnostic to the flow protocol.

An experimental protocol is developed to directly measure the new material functions revealed by medium amplitude parallel superposition (MAPS) rheology. This experimental protocol measures the medium amplitude response of a material to a simple shear deformation composed of three sine waves at different frequencies. Imposing this deformation and measuring the mechanical response reveals a rich data set consisting of up to 19 measurements of the third order complex modulus at distinct three-frequency coordinates. We discuss how the choice of the input frequencies influences the features of the MAPS domain studied by the experiment. A polynomial interpolation method for reducing the bias of measured values from spectral leakage and variance due to noise is discussed, including a derivation of the optimal range of amplitudes for the input signal. This leads to the conclusion that conducting the experiment in a stress-controlled fashion possesses a distinct advantage to the strain-controlled mode. The experimental protocol is demonstrated through measurements of the MAPS response of a model complex fluid: a surfactant solution of wormlike micelles. The resulting data set is indeed large and feature-rich, while still being acquired in a time comparable to similar medium amplitude oscillatory shear (MAOS) experiments. We demonstrate that the data represents measurements of an intrinsic material function by studying its internal consistency, its compatibility with low-frequency predictions for Coleman-Noll simple fluids, and its agreement with data obtained via MAOS amplitude sweeps. Finally, the data is compared to predictions from the corotational Maxwell model to demonstrate the power of MAPS rheology in determining whether a constitutive model is consistent with a material's time-dependent response.

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